Journal article
Polynomial bounds for chromatic number. iv: a near-polynomial bound for excluding the five-vertex path
- Abstract:
- A graph G is H-free if it has no induced subgraph isomorphic to H. We prove that a $P_5$-free graph with clique number $\omega\ge 3$ has chromatic number at most $\omega^{\log_2(\omega)}$. The best previous result was an exponential upper bound $(5/27)3^{\omega}$, due to Esperet, Lemoine, Maffray, and Morel. A polynomial bound would imply that the celebrated Erdős-Hajnal conjecture holds for $P_5$, which is the smallest open case. Thus there is great interest in whether there is a polynomial bound for $P_5$-free graphs, and our result is an attempt to approach that.
- Publication status:
- Published
- Peer review status:
- Peer reviewed
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(Preview, Version of record, pdf, 223.4KB, Terms of use)
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- Publisher copy:
- 10.1007/s00493-023-00015-w
Authors
- Publisher:
- Springer
- Journal:
- Combinatorica More from this journal
- Volume:
- 43
- Issue:
- 5
- Pages:
- 845–852
- Publication date:
- 2023-09-15
- Acceptance date:
- 2022-10-07
- DOI:
- EISSN:
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1439-6912
- ISSN:
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0209-9683
- Language:
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English
- Keywords:
- Pubs id:
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1199641
- Local pid:
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pubs:1199641
- Deposit date:
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2022-10-12
Terms of use
- Copyright holder:
- Scott et al.
- Copyright date:
- 2023
- Rights statement:
- © The Author(s) 2023. Open Access. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
- Licence:
- CC Attribution (CC BY)
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